USA domestic postage rates for first class matter were uniform and had been for decades. Other classes of mail were generally uniform as well, except when the rate change due to distances where were set in zones. Even then the postage rates within a zone were uniform. The only postage "adjustment" for difficulty in delivery was for Alaska where all parcel post matter moved at the 8th Zone (most expensive rate) no matter the distance. Everywhere else a package of parcel post had to move more than 1800 miles to be rated at Zone 8.
That all said, there has been no 2.5 cent postcard rate in effect in the USA, ever for regularly mailed postcards.
As to your comment
Eureka California it where the card was bought from the only Pharmaceutical Shop "Rings Pharmacy" north side to Sacramento. They purchased bulk post cards (100 or so) from the small post office next door on 5th street built in and around 1910. The post card displays top quality eclectic classicism dictated by area's social structure.
how did you determine that from the postcard? I can see no such indication in the photos of the card provided. Please explain.
I mentioned an International Rate book above. The same authors produced a Domestic Rate Book (from 1872 into the 21st Century) for the USA as well.
Lastly, any "provisional" or manuscript notation would be accompanied by the inclusion of the name of the post office as well as the date, at least day and month.
This "2 1/2" is in no way associated with carriage by the USPOD nor a mark supplied by the USPOD. Nor by the way was Eureka a rural region at the time. It had a population of 11,000+ with many other small towns in the nearby vicinity. Today the population is less than double that if you don't consider the Students, Facility and support staff of the California State University there. Its roots began there in 1913 as a teacher's college.
obikohaku aka Parcelpostguy